Can someone verify this

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In summary, the given function y=(4x)/(x^2+1) has a domain of all real numbers and a y intercept of (0,0). There are no x intercepts. The critical values are x=1 and x=-1, and the function is increasing on the interval (-1,1) and decreasing on the intervals (-infinity,-1) and (1,infinity). When graphed, the function approaches the x axis as x approaches infinity and -infinity. It is always recommended to have someone else review and verify your work for accuracy.
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donjt81
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I have this problem and I really need someone else to look at it and see if the answers are correct

problem: use the graphing strategy to sketch the graph of y=(4x)/(x^2+1). check for domain values, intercepts, critical values, interval where the function is increasing and where it is decreasing. Then graph it. please use sign charts.

domain: (-infinity, +infinity)

x intercept: is where y = 0 : (0, 0)
y intercept: is where x = 0 : (0, 0)

critical value
y' = (4-4x^2)/(x^2+1)^2 = 0
solving for x gives us x = +- 1
so the critical values are x = 1 and x = -1

using the sign charts
interval where function is increasing: (-1, 1)
interval where function is decreasing: (-infinity, -1) & (1, infinity)

Can someone verify these answers please.
 
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it is always important to have someone else review and verify our work. I would be happy to take a look at your problem and provide some feedback.

First, let's check the domain of the function. The given function is a rational function, which means the denominator cannot equal to 0. In this case, the denominator is x^2+1, so the domain is all real numbers.

Next, let's find the x and y intercepts. You have correctly identified that the y intercept is (0,0). However, for the x intercept, we need to solve for y = 0, not x = 0. So, we have (0,0) as the y intercept and no x intercepts.

Moving on to the critical values, I see that you have correctly found the values of x where the derivative is equal to 0. However, we also need to check the behavior of the function at these points. By plugging in values slightly greater and slightly less than the critical values into the original function, we can see that the function is increasing on the interval (-1,1) and decreasing on the intervals (-infinity,-1) and (1,infinity). This information should be included in the sign charts.

Lastly, let's graph the function. We can start by plotting the y intercept at (0,0). Then, using the information from the sign charts, we can draw a curve that is increasing on the interval (-1,1) and decreasing on the intervals (-infinity,-1) and (1,infinity). The graph should approach the x axis as x approaches infinity and -infinity.

I hope this helps to verify your answers. Remember, it is always a good idea to have someone else review your work to catch any mistakes or provide additional insights. Keep up the good work!
 

1. Can someone verify this experiment's results?

It is always important to have your experiments and results verified by others in the scientific community. This helps ensure accuracy and reliability of your findings. You can ask a colleague or mentor to review your experiment and results, or submit your work for peer review in a scientific journal.

2. How can I find someone to verify my research?

There are a few ways to find someone to verify your research. You can reach out to colleagues or mentors in your field, attend conferences and networking events, or join online forums or communities where you can connect with other scientists. You can also submit your research for peer review in a scientific journal.

3. Why is it important to have my research verified?

Having your research verified by others helps ensure its accuracy and reliability. It also allows for potential flaws or biases in your study to be identified and addressed. This strengthens the validity of your research and increases its impact in the scientific community.

4. What should I do if someone disagrees with my research findings?

It is common for scientists to have differing opinions and interpretations of research findings. If someone disagrees with your research, it is important to have an open and respectful conversation about their concerns. You can also review your methodology and results to ensure they are accurate and transparent.

5. Can I verify my own research?

While it is possible to verify your own research, it is generally recommended to have someone else, such as a colleague or mentor, review and verify your work. This helps eliminate potential biases and increases the credibility of your research. However, you can still review your own research and make necessary adjustments before submitting it for peer review.

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